Research
My research focuses on turbulent mixing in stratified flows found in our environment.
To uncover their fascinating small-scale physics, I combine experiments and mathematics.
I also developed an interest in the physics of decompression sickness in scuba diving.
Introduction
Since a picture is worth a thousand words, and a video is worth a million, I made a few short (1 to 3 minutes) videos to introduce my research into stratified flows and turbulence, why they're fascinating, and why they're important.
Introductory videos
What do I study?
Why do I find it fascinating?
Why is it important? (1/2)
Why is it important? (2/2)
Finding Nessie: an artistic view
Projects
Below is a list of my main projects (roughly in chronological order), with a dedicated image gallery that emerged from each of them. For more details check out my Publications page.
Project 1. Estimating internal wave turbulent dissipation in the deep ocean
My MSc research paper (Lefauve, Melet & Muller, 2015) tackled the turbulent dissipation of internal gravity waves generated by tides interacting with the rough seafloor in the deep, stably-stratified ocean (below the thermocline). From the seafloor these waves propagate upwards, transporting their energy, and steepening as they encounter increasing stratification. This can cause them to break turbulently, dissipating kinetic energy, and mixing the surrounding waters in sometimes highly-localised regions. This mixing is important to sustain the deep branch of the large-scale overturning circulation of the oceans.
I produced three-dimensional worlwide maps of energy dissipation by combining linear and nonlinear theories (for the wave generation, propagation, and breaking) with three global datasets: small-scale bathymetry spectral data, tidal data (from satellite altimetry) and stratification data (from Argo floats). I showed that more energy was dissipated near mid-ocean ridges in the Southern Hemisphere and that it was dissipated higher up in the water column than previously thought. I also proposed a simple method to include these results in global ocean models.
Project 2. Probing stratified turbulence with advanced experimental diagnostics and numerics
To better address the ocean mixing challenges revealed by Project 1, my PhD and postdoctoral research have then moved towards a more fundamental and experimental study of stratified turbulence. Until recently, data-rich laboratory experiments were lacking because no diagnostics were capable of measuring three-dimensional, density-dependent, small-scale turbulence, and no laboratory flow could sustain for long time periods the high levels of dissipation found in Nature. I made such experiments possible by applying state-of-the-art diagnostics to a new, highly-dissipative, canonical stratified shear flow, the stratified inclined duct (abbreviated "SID").
The new methodology, originally developed in DAMTP by S. B. Dalziel and J. L. Partridge, uses three high-speed cameras and a fast-scanning laser sheet. It allows to measure the full three-component velocity and density fields in successive two-dimensional planes, which are then combined into volumes (Partridge, Lefauve & Dalziel, 2019). I obtained 16 datasets of unprecedented quality which allowed me to develop the next two projects. Today we are still developing these measurements in the G. K. Batchelor laboratory and keep pushing the boundaries with the latest laser and high-speed camera technology.
With colleagues A. Atoufi and L. Zhu we have now also developed direct numerical simulations (DNS) of the flow in the SID (Zhu et al. 2023), which have been validated by the experiments, showing an excellent agreement which is rare enough in fluid mechanics to be highlighted. Numerical datasets have allowed us to diagnose inacessible variables such as pressure all along the duct (Atoufi et al. 2023). More recently, we have also shown that physics-informed neural networks could help us augment the resolution experimental data and provide new insights (Zhu et al. 2024).
Project 3. Waves and three-dimensional coherent structures
Using the technology from Project 2, I uncovered experimentally and explained theoretically a new three-dimensional flow structure called a ‘confined Holmboe wave’ (Lefauve et al. 2018). Holmboe waves are oscillations found in oceans and estuaries, which transport energy and mass along and across fluid layers, and which can grow unstable and trigger more vigorous mixing. I explained mathematically how the classical Holmboe instability was modified in narrow rivers channels or deep-ocean trenches which severely confine the flow laterally. The agreement between a three-dimensional stability analysis and the experimental data was astounding.
This work spurred a MSc thesis project to investigate more systematically the effects of confinement (Ducimetière et al. 2021) and a summer project on weakly nonlinear Holmboe waves to explain how these waves saturate to a finite (experimentally visible) amplitude. We developed and implemented numerically a weakly nonlinear expansion to answer this question and provide a foundation for future fully-nonlinear work (Cudby & Lefauve, 2021). I also collaborated with the UBC group of G. A. Lawrence on fully-nonlinear simulations of Holmboe waves, allowing for comparison with experiments. We focussed on the effects (or "feedback") that these waves have on the background flow through Reynolds stresses, which are central to modelling environmental flows (Yang et al. 2021).
In more recent papers (Jiang et al. 2022, 2023) we looked at the evolution of coherent vortical structures under increasing turbulence intensity, using the 16 state-of-the-art 3D datasets from Project 2. We have been able to track the how the morphology of vortices and shearing structures evolve from confined Holmboe waves to give rise to characteristic hairpin vortices. This allowed to gain new insight into how vortices stir and mix the density field in previously unsuspected ways.
Project 4. Dissipation and mixing in sustained, shear-driven stratified turbulence
One of the unique features of the stratified inclined duct (SID) experiment is that it contains the four key flow regimes observed in Nature: laminar flow, Holmboe waves, intermittent patches of turbulence, and eventually full turbulence. Much of my effort during my PhD and since has been devoted to the long-standing question: how do we predict the successive transitions to increasingly turbulent regimes?
A first milestone was the development of a hierarchy of simplified mathematical models to connect these transitions to thresholds in kinetic energy dissipation (Lefauve, Partridge & Linden, 2019). I then built on this framework to tackle turbulent mixing with a further dataset collected from 886 individual experiments covering a wide, five-dimensional parameter space which improved on decades of previous research (Lefauve & Linden, 2020). My publicly available datasets have been used by other groups, who explored applications to estuary flows.
Finally, I undertook a comprehensive statistical analysis of my previous 16 ‘state-of-the-art’ datasets from a multitude of viewpoints that speak to the experimental, numerical, and observational communities (Lefauve & Linden, 2022a, 2022b). These papers touches on the self-organisation of turbulence towards an equilibrium Richardson number, on the parameterisation using flux-gradient models and turbulent diffusivities, on mixing efficiency, and on the hierarchy of lengthscales in shear-driven stratified turbulence.
I am now trying to understand the links between 3D coherent flow structures uncovered in Project 3 and the turbulent statistics uncovered in this project. How can we link the morphological evolution of increasingly turbulent vortical and shear structures to increasing rates of turbulent production, buoyancy flux, dissipation and mixing?